Generalized Croos Validation

Convenient approximation to Leave-One-Out-Cross-Validation of a linear model $\hat{\mathbf{y}}=\mathbf{Sy}$, $\mathrm{GCV}(\hat{f})=\frac{1}{n}\sum _{i=1}^n{\left[\frac{y_i-\hat{f}(x_i)}{1-\mathrm{tr}(\mathbf{S})/n}\right]}^2\stackrel{a}{\to }\text{LOOCV}(\hat{f})$